mirt (version 0.7.0)

bfactor: Full-Information Item Bi-factor Analysis

Description

bfactor fits a confirmatory maximum likelihood bi-factor model to dichotomous and polytomous data under the item response theory paradigm. Fits univariate and multivariate 1-4PL, graded, (generalized) partial credit, nominal, multiple choice, and partially compensatory models using a dimensional reduction EM algorithm so that regardless of the number of specific factors estimated the model only uses a two-dimensional quadrature grid for integration. See confmirt for appropriate methods to be used on the objects returned from the estimation.

Usage

bfactor(data, model, quadpts = 20, SE = FALSE, verbose =
    TRUE, ...)

Arguments

data

a matrix or data.frame that consists of numerically ordered data, with missing data coded as NA

model

a numeric vector specifying which factor loads on which item. For example, if for a 4 item test with two specific factors, the first specific factor loads on the first two items and the second specific factor on the last two, then the vector is

quadpts

number of quadrature points per dimension (default 20).

SE

logical; calculate information matrix and standard errors?

verbose

logical; print observed log-likelihood value at each iteration?

...

additional arguments to be passed to the main estimation function. See mirt for more details

Details

bfactor follows the item factor analysis strategy explicated by Gibbons and Hedeker (1992) and Gibbons et al. (2007). Nested models may be compared via an approximate chi-squared difference test or by a reduction in AIC or BIC (accessible via anova). See mirt for more details regarding the IRT estimation approach used in this package.

References

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29.

Gibbons, R. D., & Hedeker, D. R. (1992). Full-information Item Bi-Factor Analysis. Psychometrika, 57, 423-436.

Gibbons, R. D., Darrell, R. B., Hedeker, D., Weiss, D. J., Segawa, E., Bhaumik, D. K., Kupfer, D. J., Frank, E., Grochocinski, V. J., & Stover, A. (2007). Full-Information item bifactor analysis of graded response data. Applied Psychological Measurement, 31, 4-19

See Also

expand.table, key2binary, confmirt.model, mirt, confmirt, bfactor, multipleGroup, mixedmirt, wald, itemplot, fscores, fitIndices, extract.item, iteminfo, testinfo, probtrace, boot.mirt, imputeMissing, itemfit, mod2values, read.mirt, simdata, createItem

Examples

###load SAT12 and compute bifactor model with 3 specific factors
data(SAT12)
data <- key2binary(SAT12,
  key = c(1,4,5,2,3,1,2,1,3,1,2,4,2,1,5,3,4,4,1,4,3,3,4,1,3,5,1,3,1,5,4,5))
specific <- c(2,3,2,3,3,2,1,2,1,1,1,3,1,3,1,2,1,1,3,3,1,1,3,1,3,3,1,3,2,3,1,2)
mod1 <- bfactor(data, specific)
summary(mod1)

###Try with fixed guessing parameters added
guess <- rep(.1,32)
mod2 <- bfactor(data, specific, guess = guess)
coef(mod2)

#########
#simulate data
a <- matrix(c(
1,0.5,NA,
1,0.5,NA,
1,0.5,NA,
1,0.5,NA,
1,0.5,NA,
1,0.5,NA,
1,0.5,NA,
1,NA,0.5,
1,NA,0.5,
1,NA,0.5,
1,NA,0.5,
1,NA,0.5,
1,NA,0.5,
1,NA,0.5),ncol=3,byrow=TRUE)

d <- matrix(c(
-1.0,NA,NA,
-1.5,NA,NA,
 1.5,NA,NA,
 0.0,NA,NA,
2.5,1.0,-1,
3.0,2.0,-0.5,
3.0,2.0,-0.5,
3.0,2.0,-0.5,
2.5,1.0,-1,
2.0,0.0,NA,
-1.0,NA,NA,
-1.5,NA,NA,
 1.5,NA,NA,
 0.0,NA,NA),ncol=3,byrow=TRUE)
items <- rep('dich', 14)
items[5:10] <- 'graded'

sigma <- diag(3)
dataset <- simdata(a,d,2000,itemtype=items,sigma=sigma)

specific <- c(rep(1,7),rep(2,7))
simmod <- bfactor(dataset, specific)
coef(simmod)